Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Yang Zhijian¹  Li Xiao¹ 

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Peoples R China

关键词: Initial-boundary value problem;    Kirchhoff equation;    Infinite-dimensional dynamical system;    Global attractor;    Exponential attractor;   

DOI  :  10.1016/j.jmaa.2010.09.051

来源: Elsevier

【 摘 要 】

The paper studies the existence of the finite-dimensional global attractors and exponential attractors for the dynamical system associated with the Kirchhoff type equation with a strong dissipation u(tt) M(parallel to del u parallel to(2))Delta u - Delta u(t) + h(u(t)) + g(u) = f(x). It proves that the above mentioned dynamical system possesses a global attractor which has finite fractal dimension and an exponential attractor. For application, the fact shows that for the concerned viscoelastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space, and the dimension of the attractor, that is, the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow, is finite. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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